Filtering with Wavelet Zeros and Gaussian Analytic Functions

We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propose a methodology that detects components of a signal in white noise based on the distribution of the zeros of its continuous WT. To illustrate that the continuous theory can be employed in a discrete setting, we establish a uniform convergence result for the discretized continuous WT and apply the proposed method to a variety of acoustic signals.